To find the perimeter of the polygon with the given points, we need to determine the distance between consecutive points and then sum these distances.

The points provided are:

• $A(-1, 3)$
• $B(4, 3)$
• $C(4, 0)$
• $D(-1, 0)$

These points form a rectangle because opposite sides are parallel and equal in length.

Step 1: Calculate the distance between each pair of consecutive points.

1. Distance between $A(-1, 3)$ and $B(4, 3)$:

   Since both points have the same $y$-coordinate (3), the distance is simply the difference in the $x$-coordinates: $AB = |4 - (-1)| = 5$

2. Distance between $B(4, 3)$ and $C(4, 0)$:

   Since both points have the same $x$-coordinate (4), the distance is simply the difference in the $y$-coordinates: $BC = |3 - 0| = 3$

3. Distance between $C(4, 0)$ and $D(-1, 0)$:

   Since both points have the same $y$-coordinate (0), the distance is simply the difference in the $x$-coordinates: $CD = |4 - (-1)| = 5$

4. Distance between $D(-1, 0)$ and $A(-1, 3)$:

   Since both points have the same $x$-coordinate (-1), the distance is simply the difference in the $y$-coordinates: $DA = |3 - 0| = 3$

Step 2: Sum the distances to find the perimeter.

$\text{Perimeter} = AB + BC + CD + DA = 5 + 3 + 5 + 3 = 16$

Thus, the perimeter of the polygon is 16 units.

Would you like more details or have any questions?

Here are five related questions you might find interesting:

1. How would you find the area of the same polygon?
2. What if the polygon were a different shape, like a trapezoid—how would you approach the perimeter then?
3. How do you find the perimeter of a polygon with more than four sides?
4. How would the process change if the points were in 3D space instead of 2D?
5. How do you find the perimeter of a circle or an ellipse?

Tip: Remember, when calculating distances between points in a 2D plane, it's often easiest to check if the points are horizontally or vertically aligned to simplify your calculations.